5 papers
Morley Simplices in Higher Dimensions: Regularity, Reflections, and Counterexamples
Quang Hung Tran
Trisecting the dihedral angles of an -simplex defines its Morley simplex. We study the original simplices for which this simplex is regular. A criterion in terms of the Gram mat…
The Converse Problem for the Morley Tetrahedron: Counterexamples, Conjectures, and Partial Results
Quang Hung Tran
In a paper in Acta Mathematica Hungarica the author proved that the Morley tetrahedron of an isosceles tetrahedron, obtained by trisecting the six dihedral angles, is again isoscel…
Some properties of rectangle and a random point
Quang Hung Tran
We establish a relationship between the two important central lines of the triangle, the Euler line and the Brocard axis, in a configuration with an arbitrary rectangle and a rando…
A family of weighted Erdős-Mordell inequality and applications
Tran Quang Hung
We establish some new generalizations of Erdős-Mordell inequality by adding weights to its terms. Using these generalizations, we derived strengthened versions of the original Erdő…
Some Constructions of the Golden Ratio in an Arbitrary Triangle
Quang Hung Tran
We establish some new constructions of the golden ratio in an arbitrary triangle using symmedians and nine-point circle.